"Milk It for All It's Worth" or "Milk It for All Its Worth"?

My sister just asked me (being an English major) whether the phrase is "milk it for all it's worth" or "milk it for all its worth." It seems she typed the "it's" version into Word, which promptly told her to take out the apostrophe. Knowing that the corrective powers of Word’s grammatical system can sometimes be faulty, she passed the question on to me. I am, obviously, of no help to her in this matter.

Neither of us can decide if we should milk something for all it is worth, or milk something for the inherent worth within it. Both options seem plausible.